How can I change Blender's output image resolution?
For texture backing the resolution of the target image is what's important. The first step for baking is to create a new image in the image viewer were the normal map will be stored.  Here you can set your desired resolution.  If you use cycles, you need to add the texture node to the material of the object you want to bake to and select the image you just created. Next you can go to the bake settings in the render tab, mark selected to active. Make sure you select the objects in the scene, the one that you want to bake to needs to be selected last (it has a bright orange outline). Then you can press the bake button and once it is finished, save the image from the image viewer.